I am in my third year of teaching secondary Mathematics here in Michigan. This year’s junior class is required to successfully complete four years of high school Mathematics. They are expected to pass Algebra I, Geometry, Algebra II, and an additional mathematics credit. I am sure you have heard the old house analogy when someone was speaking of the scaffolding present in the curriculum. Students do need to build on prior knowledge to climb through the content. The core content of algebra requires students to represent functions in a myriad of ways. Students begin with linear functions and advance to quadratics and beyond. The concept of a function is integral to the mastery of knowledge in secondary and post-secondary Mathematics.
In chapter six of their math standards, the National Council of Teachers of Mathematics (NCTM) states “Functions are one of the most important mathematical tools for helping students make sense of the world around them, as well as preparing them for further study in mathematics (Yerushalmy and Shternberg 2001). Functions appear in most branches of mathematics and provide a consistent way of making connections between and among topics. Students’ continuing development of the concept of function must be rooted in reasoning, and likewise functions are an important tool for reasoning. Thus, developing procedural fluency in using functions is a significant goal of high school mathematics. (41)”
Students begin to question how the content covered relates to their own lives as they progress through these courses. The content requires students to master skills and knowledge that the students feel have little or no relevance to their own lives. I feel that the compelling problem of practice that I want to address in this TechQuest is: How can I help students identify the function that is best suited for modeling a given real-world situation? This is Algebra I content expectation A2.4.1, but is a core content piece throughout Algebra II, Trigonometry, and Pre-Calculus Courses. Students learn in various ways and I am searching for some technology that will help me incorporate many different pedagogical strategies. In their book Technology and to Support Learning, Bransford and Cocking state “Technology can help create an active environment in which students not only solve their own problems, but also find their own problems (Bransford 195). I am hoping to find technology that helps me create an active situation where real student learning can take place. In my own experience, I have developed related lessons that students can master the content temporarily, but cannot reproduce the content later down the line. For example, the student may be able to complete similar tasks during an Algebra II course, but will experience difficulty with a related activity once they have entered Pre-Calculus and are taking a pre-assessment. I want my students to have a memorable experience that will generate real learning related to this subject matter.
Casey, what a great description of the problem of practice you want to address. I think you are speaking for all math teachers here. I like how you've thoughtfully narrowed down high school math content to a fundamental concept: the function. I look forward to your thoughts on which technology to use here, and how it should be implemented. Great start!
ReplyDeleteSadly, I'm horrible with math even though I took advanced classes in high school. I didn't have the best teachers and we never incorporated technology in any way (other then graphing calculators - which drove me crazy because I never knew what my teacher was pressing to get the answers!) I look forward to see how you incorporate technology here. My sister is a math teacher at Rochester High School so I have much respect for the challenges involved with the new grad requirements.
ReplyDeleteI remember my math experience in high school didn't really fully bear fruits until I began seeing working digital models in my AP physics and AP Chem classes. I remember that as soon as I could see how different variables could manipulate curves I began to see and predict patterns. I thought it was pretty cool using math as an easy way to make a grounded prediction. As a result of the science ideas I got a better idea of the math. Im sure that expanding this and using it in math will yeild some great results!
ReplyDeleteI would have to agree with Karen! I had the same misfortune with math teachers - especially while in high school. I applaud your effort in wanting to give your students "a memorable experience that will generate real learning related to this subject matter." You have done an outstanding job of defining the educational problem you hope to address, as well as the related curriculum content area=8-) I'm looking forward to learning which technology you elect to use for your project.
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